Weighted oscillator strengths and lifetimes for the S IX and S X spectra

The weighted oscillator strengths (gf) and the lifetimes presented in this work were carried out in a multi configuration Hartree-Fock relativistic (HFR) approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure, in order to improve the adjustment to experimental energy levels. This method produces gf-values that are in better agreement with intensity observations and lifetime values that are closer to the experimental ones. In this work, we presented all the experimentally known electric dipole S IX and S X spectral lines.     

Analysis of the charge transfer mechanisms responsible for the current-voltage characteristics of Ca<Subscript>4</Subscript>Ga<Subscript>2</Subscript>S<Subscript>7</Subscript>: Eu<Superscript>3+</Superscript> single crystals

The current-voltage characteristics of Ca₄Ga₂S₇: Eu³⁺ single crystals are measured for the first time, and the processes affecting these characteristics are analyzed theoretically. It is demonstrated that Ca₄Ga₂S₇: Eu³⁺ single crystals are high-resistance semiconductors with a resistivity of ～10⁹ Ω cm and a relative permittivity of 10.55. The electrical properties of the studied materials are governed by traps with activation energies of 0.13 and 0.19 eV and a density ranging from 9.5×10¹⁴ to 2.7×10¹⁵ cm^?3. The one-carrier injection is observed in weak electric fields. In electric fields with a strength of more than 4×10³ V/cm, traps undergo thermal field ionization according to the Pool-Frenkel mechanism. At low temperatures and strong fields (160 K and 5×10⁴ V/cm), the electric current is most likely due to hopping conduction by charge carriers over local levels in the band gap in the vicinity of the Fermi level.     

Consequences of weak absorption in light heavy-ion reactions: Molecular resonances and nuclear rainbows

In the elastic angular distributions of the systems composed of tightly bound α-nuclei, ¹²C+¹²C, ¹⁶O+¹⁶O and ¹⁶O+¹²C, the higher-order Airy minima are observed in the energy region between 5 and 10 MeV per nucleon. The obtained optical potentials are deeply attractive and with incomplete absorption. The same potentials successfully describe the lower-energy (molecular resonances) and the higher-energy (first Airy minimum) data.     

Numerical determination of the density profile of an inhomogeneous membrane: solution of the inverse vibration problem

Given one or more vibrational modes of a membrane, the free vibration equation can be applied to infer the mass surface density. This paper considers determining the surface density of an inhomogeneous membrane from digitized holographic projections (interferograms) of the modeshapes. Spatially discrete numerical models of the membrane surface are presented, which can be used to solve both forward and inverse vibration problems. The accuracy of the discrete models is examined for exactly solvable free vibration problems involving inhomogeneous membranes. For the solution of the inverse problem, error estimates are given for the mass surface density deduced from modeshape interferograms. The practicability of the method is investigated using simulated experimental data for membranes with composite and continuously inhomogeneous density profiles. Strategies are discussed for reducing errors in the reconstructed densities.     

Crack path instabilities in DCDC experiments in the low speed regime

We studied the low speed fracture regime (10⁻⁴-10⁻⁹ m s⁻¹) in different glassy materials (soda-lime glass, glass ceramics) with variable but controlled length scale of heterogeneity. The chosen mechanical system enabled us to work in pure mode I (tensile) and at a fixed load on double cleavage drilled compression specimen. The internal residual stresses of studied samples were carefully relaxed by appropriate thermal treatment. By means of optical and atomic force microscopy techniques fracture surfaces have been examined. We have shown for the first time that the crack front line underwent an out-of-plane oscillating behavior as a result of a reproducible sequence of instabilities. The wavelength of such a phenomenon is in the micrometer range and its amplitude in the nanometer range. These features were observed for different glassy materials providing that a typical length scale characterizing internal heterogeneities was lower than a threshold limit estimated to few nanometers. This effect is the first clear experimental evidence of crack path instabilities in the low speed regime in a uniaxial loading experiment. This phenomenon has been interpreted by referring to the stability criterion for a straight crack propagation as presented by Adda-Bedia et al. [Phys. Rev. Lett. 76 (1996) 1497].     

Note on a conjecture of toft

A conjecture of Toft [17] asserts that any 4-critical graph (or equivalently, every 4-chromatic graph) contains a fully odd subdivision ofK ₄. We show that if a graphG has a degree three nodev such thatG-v is 3-colourable, then eitherG is 3-colourable or it contains a fully oddK ₄. This resolves Toft's conjecture in the special case where a 4-critical graph has a degree three node, which is in turn used to prove the conjecture for line-graphs. The proof is constructive and yields a polynomial algorithm which given a 3-degenerate graph either finds a 3-colouring or exhibits a subgraph that is a fully odd subdivision ofK ₄. (A graph is 3-degenerate if every subgraph has some node of degree at most three.)